A Simplified FRI Sampling System for Pulse Streams Based on Constraint Random Modulation

The recent finite rate of innovation (FRI) framework provides effective sub-Nyquist sampling of pulse streams, allowing recovery of such signals from a set of Fourier coefficients. In this brief, a multi-channel FRI sampling system is presented to sample distinct bands of Fourier coefficients. This is achieved through modulating the desired spectrum band to baseband and then filtering with a low-pass filter. However, the modulation process will lead to the spectrum aliasing and unavailability. A modulation frequency selection strategy is proposed to solve this problem, which allows obtaining reconfigurable Fourier coefficients from the aliasing spectrum. Combining with multi-channel structure, we present a simple and efficient way to sample distinct bands of the pulse streams’ spectrum. Finally, a design and implementation of the hardware prototype is presented. Simulation and hardware experiment results demonstrate the effectiveness and robustness of our system.